I am studying “Rosenberg’s Analytical Dynamics of Discrete Systems”. In chapter 4, he discussed on holonomic and nonholonomic constraints. At the end of the chapter, he asked a question that confused me:
“Particle P can move on the bottom of a two-dimensional cage. Since the position of the particle can be described by the two coordinates x and y, or by the three coordinates $\theta$, $\phi$ and $\xi$, it seems that the latter must satisfy a constraint relation between them. Can you find that relation? How many degrees of freedom does the particle have?”
If we use $\theta$, $\phi$ and $\xi$ to describe the position of P, it means P has three degree of freedom. In the contrary, because of planar motion of the particle P, there are utmost two degree of freedom. It seems paradoxical. What is my mistake?